Advanced studies on Simulation Methodologies for very Complicated Fracture Phenomena

Abstract

Although nowadays, computational techniques are well developed, for Extremely Complicated Fracture Phenomena, they are still very difficult to simulate, for general engineers, researchers. To overcome many difficulties in those simulations, we have developed not only Simulation Methodologies but also theoretical basis and concepts. We sometimes observe extremely complicated fracture patterns, especially in dynamic fracture phenomena such as dynamic crack branching, kinking, curving, etc. For examples, although the humankind, from primitive men to modern scientists such as Albert Einstein had watched the post-mortem patterns of dynamic crack branching, the governing condition for the onset of the phenomena had been unsolved until our experimental study. From in these studies, we found the governing condition of dynamic crack bifurcation, as follows. When the total energy flux per unit time into a propagating crack tip reaches the material crack resistance, the crack braches into two cracks [total energy flux criterion]. The crack branches many times whenever the criterion is satisfied. Furthermore, the complexities also arise due to their time-dependence and/or their-deformation dependence. In order to make it possible to simulate such extremely complicated fracture phenomena, we developed many original advanced computational methods and technologies. These are (i)moving finite element method based on Delaunay automatic triangulation (MFEMBOAT), path independent,(ii) equivalent domain integral expression of the dynamic J integral associated with a continuous auxiliary function,(iii) Mixed phase path-prediction mode simulation, (iv) implicit path prediction criterion. In this paper, these advanced computational methods are thoroughly explained together with successful comparison with the experimental results. Since multiple dynamic crack branching phenomena may be most complicated fracture due to complicated fracture paths, and its time dependence (transient), this simulation and numerical results are mainly explained.